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Results (8 matches)

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Label Class Base field Conductor norm Rank Torsion CM Sato-Tate Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
9.1-a1 9.1-a \(\Q(\sqrt{17}) \) \( 3^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $15.98892188$ 0.969470791 \( -\frac{396321250}{3} a + 338397375 \) \( \bigl[1\) , \( -a\) , \( a + 1\) , \( 48 a - 123\) , \( 291 a - 749\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(48a-123\right){x}+291a-749$
81.1-c1 81.1-c \(\Q(\sqrt{17}) \) \( 3^{4} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $6.828410025$ 0.414033173 \( -\frac{396321250}{3} a + 338397375 \) \( \bigl[1\) , \( -1\) , \( 1\) , \( 435 a - 1115\) , \( -7202 a + 18448\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(435a-1115\right){x}-7202a+18448$
144.4-c1 144.4-c \(\Q(\sqrt{17}) \) \( 2^{4} \cdot 3^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $25.59440343$ 0.775944329 \( -\frac{396321250}{3} a + 338397375 \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 117 a - 300\) , \( -876 a + 2244\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(117a-300\right){x}-876a+2244$
144.5-c1 144.5-c \(\Q(\sqrt{17}) \) \( 2^{4} \cdot 3^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $3.199300429$ 0.775944329 \( -\frac{396321250}{3} a + 338397375 \) \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -119 a - 186\) , \( -1469 a - 2294\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-119a-186\right){x}-1469a-2294$
576.6-e1 576.6-e \(\Q(\sqrt{17}) \) \( 2^{6} \cdot 3^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.978485520$ $7.242622550$ 3.437603564 \( -\frac{396321250}{3} a + 338397375 \) \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 100 a - 256\) , \( -813 a + 2081\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(100a-256\right){x}-813a+2081$
576.6-n1 576.6-n \(\Q(\sqrt{17}) \) \( 2^{6} \cdot 3^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.209789527$ $18.09797622$ 1.841701975 \( -\frac{396321250}{3} a + 338397375 \) \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -19 a - 36\) , \( 66 a + 110\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-19a-36\right){x}+66a+110$
576.7-e1 576.7-e \(\Q(\sqrt{17}) \) \( 2^{6} \cdot 3^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.978485520$ $7.242622550$ 3.437603564 \( -\frac{396321250}{3} a + 338397375 \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -101 a - 157\) , \( -1084 a - 1693\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-101a-157\right){x}-1084a-1693$
576.7-n1 576.7-n \(\Q(\sqrt{17}) \) \( 2^{6} \cdot 3^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $3.356632445$ $2.262247028$ 1.841701975 \( -\frac{396321250}{3} a + 338397375 \) \( \bigl[a\) , \( 1\) , \( a\) , \( 21 a - 61\) , \( 93 a - 253\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(21a-61\right){x}+93a-253$
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  *The rank, regulator and analytic order of Ш are not known for all curves in the database; curves for which these are unknown will not appear in searches specifying one of these quantities.